Solve the Absolute Value Inequality for b |b+4|-2=4

$| b + 4 | - 2 = 4$

Move all terms not containing $| b + 4 |$ to the right side of the equation.

Add $2$ to both sides of the equation.

$| b + 4 | = 4 + 2$

Add $4$ and $2$ .

$| b + 4 | = 6$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$b + 4 = \pm 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$b + 4 = 6$

Move all terms not containing $b$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$b = 6 - 4$

Subtract $4$ from $6$ .

$b = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$b + 4 = - 6$

Move all terms not containing $b$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$b = - 6 - 4$

Subtract $4$ from $- 6$ .

$b = - 10$

The complete solution is the result of both the positive and negative portions of the solution.

$b = 2, - 10$